Long-range low-power communications are starting to replace short-range low-power communications in monitoring applications based on wireless sensor networks, both in rural and urban environments, due to the small deployment cost of long-range technologies. In this paper, we focus on the MAC layer of the recent LoRaWAN (long-range wide area network) standard, and specifically on the on-the-air activation procedure, which defines how nodes join an existing network. We propose a Markov chain model of the on-the-air activation, and we derive the expected delay and the expected energy required to join the network. We analyze the impact of several parameters on these metrics, including traffic conditions, duty cycles, and channel availability. We also discuss the impact of the regional settings of the standard. To the best of our knowledge, this is the first analysis of the MAC layer of LoRaWAN.